Three-dimensional black holes and Liouville field theory

Toshio Nakatsu, Hiroshi Umetsu, Naoto Yokoi

研究成果: Article査読

16 被引用数 (Scopus)


A quantization of (2 + 1)-dimensional gravity with negative cosmological constant is presented, and it is used to study quantum aspects of (2 + 1)-dimensional black holes. The quantization consists of two procedures. One is related with quantization of the asymptotic Virasoro symmetry. The concept of the Virasoro deformation of 3-geometry is introduced. For a given black hole, the deformation of the exterior of the outer horizon is identified with a product of the appropriate coadjoint orbits of the Virasoro groups diffS1±. Its quantization provides unitary irreducible representations of the Virasoro algebra, in which the state of the black hole becomes primary. To make the quantization complete, holonomies, the global degrees of freedom, are taken into account. By an identification of these topological operators with zero modes of the Liouville field, the aforementioned unitary representations are shown, as long as c ≫ 1, to be the Hilbert space of this two-dimensional conformal field theory. This conformal field theory, living on the cylinder at infinity of the black hole and having continuous spectra, can recognize the outer horizon only as a one-dimensional object in SL2(R) and realize it as insertions of the corresponding vertex operator. Therefore it cannot be a conformal field theory on the horizon. Two possible descriptions of the horizon conformal field theory are proposed.

ジャーナルProgress of Theoretical Physics
出版ステータスPublished - 1999 10

ASJC Scopus subject areas

  • 物理学および天文学(その他)


「Three-dimensional black holes and Liouville field theory」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。